Yves Capdeboscq

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Here n denotes the unit outward normal to the domain Ω. Let ω denote a set of “inhomogeneities” inside Ω. The geometric assumptions about the set of “inhomogeneities” are very simple: we suppose the set ω is measurable, and separated away from the boundary, (i.e., dist(ω , ∂Ω) > d0 > 0). Most importantly, we suppose that 0 < |ω | gets arbitrarily small,(More)
This paper presents a new algorithm for conductivity imaging. Our idea is to extract more information about the conductivity distribution from data that have been enriched by coupling impedance electrical measurements to localized elastic perturbations. Using asymtotics of the elds in the presence of small volume inclusions, we relate the pointwise values(More)
In earlier work [8] we have derived a very general representation formula for the voltage perturbation caused by volumetrically small inhomogeneities in an otherwise known conductor. The ingredients of this formula are (1) a limiting probability measure, (2) a “background” fundamental solution, and (3) an “effective” polarization tensor. In [9] we proved(More)
We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction (cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of(More)
In this paper, we show that using microwave measurements at different frequencies and ultrasound localized perturbations to create local changes in the medium it is possible to extend the method developed by Ammari et al. in [3] to problems in the form { ∇ · (a∇u) + k2qu = 0 in Ω, u = φ on ∂Ω, and to reconstruct reliably both the real-valued functions a and(More)
This paper is concerned with the homogenization of an eigenvalue problem in a periodic heterogeneous domain for the multigroup neutron di€usion system. Such a model is used for studying the criticality of nuclear reactor cores. We prove that the ®rst eigenvector of the multigroup system in the periodicity cell controls the oscillatory behaviour of the(More)
We make progress towards proving the strong Eshelby’s conjecture in three dimensions. We prove that if for a single nonzero uniform loading the strain inside inclusion is constant and further the eigenvalues of this strain are either all the same or all distinct, then the inclusion must be of ellipsoidal shape. As a consequence, we show that for two(More)
Elliptic regularity theory applied to time harmonic anisotropic Maxwell's equations with less than Lipschitz complex coefficients The focus of this paper is the study of the regularity properties of the time harmonic Maxwell's equations with anisotropic complex coefficients, in a bounded domain with C 2,1 boundary. We assume that at least one of the(More)